A sprinter explodes out of the starting block with an acceleration of +2.3 m/s^2, which she sustains for 1.2 s. Then, her acceleration drops to zero for the rest of the race. What is her velocity (a) at t=1.2 s ans (b) at the end of the race?
a. V = 2.3m/s^2 * 1.2s = 2.76m/s.
b. Since the acceleration dropped to
0 at 1.2 sec, the velocity remained
constant at 2.76m/s.
thankyou soo much!!!
Oh, the thrilling world of sprinting! Let's calculate the velocity of our speedy sprinter.
(a) At t=1.2 s, we first need to find out how far she traveled during that time with a constant acceleration of +2.3 m/s^2. Using the formula s = ut + 0.5at^2, where u is the initial velocity, t is time, a is acceleration, and s is displacement, we can calculate the displacement.
Since she starts from rest (u = 0), the displacement during this time is given by s = 0.5at^2. Plugging in the values, we get s = 0.5 * 2.3 * (1.2)^2 = 1.7256 meters.
Now, we can calculate her velocity at t=1.2 s using the equation v = u + at, which becomes v = 0 + 2.3 * 1.2 = 2.76 m/s. So, her velocity at t=1.2 s is 2.76 m/s.
(b) Since her acceleration drops to zero for the rest of the race, her velocity remains constant after t=1.2 s. Therefore, her velocity at the end of the race will be the same as her velocity at t=1.2 s, which is 2.76 m/s.
Now, isn't it wonderful how physics can explain the exhilaration of sprinting? Keep running towards your dreams, my friend!
To find the velocity of the sprinter, we can use the equations of motion. Let's break down the problem into two parts:
(a) From the start until t = 1.2 s (when the acceleration is +2.3 m/s^2)
(b) From t = 1.2 s until the end of the race (when the acceleration is 0)
(a) From t = 0 to t = 1.2 s:
We are given the acceleration (a1 = +2.3 m/s^2) and the time (t1 = 1.2 s). We can use the equation:
v = u + at
where:
- v is the final velocity
- u is the initial velocity (which is typically 0 when starting from rest)
- a is the acceleration
- t is the time
Since the sprinter starts from rest, the initial velocity u is 0. Plugging in the values, we have:
v1 = 0 + a1 * t1
v1 = 0 + 2.3 * 1.2
Calculate the value to find v1.
(b) From t = 1.2 s until the end of the race:
Now, the acceleration is 0 (a2 = 0), which means there is no force acting on the sprinter. We can use the equation:
v = u + at
Since the acceleration is 0, the sprinter's velocity remains constant after t = 1.2 s. Therefore, the final velocity v2 will be the same as the velocity at t = 1.2 s, which we calculated as v1 in the previous step.
So, the sprinter's velocity at the end of the race (t = end of the race) is also v2.
By following these steps, you can find the answers to your questions.